It is normal in the art of floating point arithmetic and logic units to normalize operands to a standard, such as IEEE standard P754. By adopting a standard, the range of numbers upon which computations can be made is limited beyond the physical limitations of the processor performing the computations. Thus, the minimum order of magnitude of a number will be limited by the exponent (exp.=0), whereas in fact a lower order of magnitude number could be handled by having a denormalized mantissa (i.e. one having one or more leading zeros).
A problem with handling denormalized numbers is that, depending on the computations, a normalization step is generally required at the end of the computation. In the case of subtraction computations, even in the case where the two operands are normalized, the result is frequently denormalized. For example, if the number 1.00101 is subtracted from 1.00110, the result is 0.00001. This result requires normalization. If normalization of a number having a low exponent is carried out automatically, there may be `excess` normalization in the sense that a negative exponent results and a further denormalization step is still required to provide the desired result.